a painter needs to cover a triangular region 60 meters by 68 meters by 71 meters. a can of paint covers 70 square meters. how many cans will be needed?
Looks like Heron's formula is best here to get the area.
Then, divide that by 70m^2/gal to get the # gallons.
To find out how many cans of paint are needed to cover the triangular region, we first need to calculate the total area of the triangular region.
The area of a triangle can be found using Heron's formula, which states that the area of a triangle with side lengths a, b, and c is given by:
Area = sqrt(s * (s - a)*(s - b)*(s - c))
where s is the semi-perimeter (s = (a + b + c) / 2).
In this case, the side lengths are 60 meters, 68 meters, and 71 meters. So we can calculate the semi-perimeter as:
s = (60 + 68 + 71) / 2 = 199 / 2 = 99.5 meters
Next, we can substitute the values into the formula to calculate the area of the triangular region:
Area = sqrt(99.5 * (99.5 - 60)*(99.5 - 68)*(99.5 - 71))
= sqrt(99.5 * 39.5 * 31.5 * 28.5)
= sqrt(7,875,651.875)
≈ 2,805.51 square meters
Now, we know that each can of paint covers 70 square meters. To find out how many cans we need to cover 2,805.51 square meters, we can divide the total area by the area covered by each can:
Number of cans = 2,805.51 / 70
≈ 40.08 cans
Since we can't have a fraction of a can, we round up to the nearest whole number. Therefore, the painter will need approximately 41 cans of paint to cover the triangular region.